Economic growth and economic development 510

Introduction to Modern Economic Growth
assume that AF (t) evolves exogenously according to the differential equation
A˙ F (t)
= gF ,
AF (t)
with initial condition AF (0) > 0.
Let the human capital of the workforce be denoted by h. Notice that this human
capital does not feature in the production function, (10.43). This is an extreme case
in which human capital does not play any of the productivity enhancing role we
have emphasized so far. Instead, the role of human capital in the current model will
be to facilitate the implementation and use of frontier technology in the production
process. In particular, the evolution of the technology in use, A (t), is governed by
the differential equation
A˙ (t) = gA (t) + φ (h) AF (t) ,
with initial condition A (0) ∈ (0, AF (0)). The parameter g is strictly less than gF

and measures the growth rate of technology A (t), resulting from learning by doing
or other sources of productivity growth. But this is only one source of improvements
in technology. The other one comes from the second term, and can be interpreted
as improvements in technology because of implementation and adoption of frontier
technologies. The extent of this second source of improvement is determined by the
average human capital of the workforce, h. This captures the above-mentioned role
of human capital, in facilitating coping with technological change. In particular, we
assume that φ (·) is increasing, with
¯
φ (0) = 0 and φ (h) = gF − g > 0 for all h ≥ h,
¯ > 0. This specification implies that the human capital of the workforce
where h
regulates the ability of the economy to cope with new developments embedded in
the frontier technologies; if the workforce has no human capital, there will be no
adoption or implementation of frontier technologies and A (t) will grow at the rate g.

¯ there will be very quick adaptation to the frontier technologies.
If, in contrast, h ≥ h,
Since AF (t) = exp (gF t) AF (0), the differential equation for A (t) can be written

as
A˙ (t) = gA (t) + φ (h) AF (0) exp (gF t) .
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